a question driven socio-hydrological modeling process · human and hydrological systems are...

Hydrol Earth Syst Sci 20 73ndash92 2016

wwwhydrol-earth-syst-scinet20732016

doi105194hess-20-73-2016

copy Author(s) 2016 CC Attribution 30 License

A question driven socio-hydrological modeling process

M Garcia1 K Portney2 and S Islam13

1Civil amp Environmental Engineering Department Tufts University 200 College Avenue Medford MA 02155 USA2Bush School of Government amp Public Service Texas AampM University 4220 TAMU College Station TX 77843 USA3The Fletcher School of Law and Diplomacy Tufts University 160 Packard Avenue Medford MA 02155 USA

Correspondence to M Garcia (margaretgarciatuftsedu)

Received 29 July 2015 ndash Published in Hydrol Earth Syst Sci Discuss 24 August 2015

Revised 1 December 2015 ndash Accepted 7 December 2015 ndash Published 15 January 2016

Abstract Human and hydrological systems are coupled hu-

man activity impacts the hydrological cycle and hydrological

conditions can but do not always trigger changes in human

systems Traditional modeling approaches with no feedback

between hydrological and human systems typically cannot

offer insight into how different patterns of natural variabil-

ity or human-induced changes may propagate through this

coupled system Modeling of coupled humanndashhydrological

systems also called socio-hydrological systems recognizes

the potential for humans to transform hydrological systems

and for hydrological conditions to influence human behavior

However this coupling introduces new challenges and exist-

ing literature does not offer clear guidance regarding model

conceptualization There are no universally accepted laws of

human behavior as there are for the physical systems further-

more a shared understanding of important processes within

the field is often used to develop hydrological models but

there is no such consensus on the relevant processes in socio-

hydrological systems Here we present a question driven pro-

cess to address these challenges Such an approach allows

modeling structure scope and detail to remain contingent

on and adaptive to the question context We demonstrate the

utility of this process by revisiting a classic question in wa-

ter resources engineering on reservoir operation rules what

is the impact of reservoir operation policy on the reliabil-

ity of water supply for a growing city Our example model

couples hydrological and human systems by linking the rate

of demand decreases to the past reliability to compare stan-

dard operating policy (SOP) with hedging policy (HP) The

model shows that reservoir storage acts both as a buffer for

variability and as a delay triggering oscillations around a sus-

tainable level of demand HP reduces the threshold for action

thereby decreasing the delay and the oscillation effect As

a result per capita demand decreases during periods of wa-

ter stress are more frequent but less drastic and the additive

effect of small adjustments decreases the tendency of the sys-

tem to overshoot available supplies This distinction between

the two policies was not apparent using a traditional noncou-

pled model

1 Introduction

Humans both respond to and ignore changes in environmen-

tal conditions While humans depend on the natural hydro-

logical cycle to supply water for both personal and eco-

nomic health (Falkenmark 1977) they also depend on an

array of other natural and human resources to maintain and

grow communities At times water availability can act as the

limiting constraint locally preventing or stalling the expan-

sion of human activity For example water availability and

variability constrained agricultural development in the Tarim

River basin in western China before major water storage and

transport infrastructure was constructed (Liu et al 2014) At

other times the water-related risks rise in the background

disconnected from decision making while other priorities

prevail For instance the level of the Aral Sea has continued

to decline for decades imposing significant costs on adjacent

communities but no coordinated effort to stop the decline

emerged (Micklin 2007) At still other times public policy

decisions may work to exacerbate water problems as when

decisions are made to keep municipal water prices artificially

low or when ldquosenior water rightsrdquo encourage water usage in

the face of shortages (Chong and Sunding 2006 Hughes et

al 2013 Mini et al 2014)

Published by Copernicus Publications on behalf of the European Geosciences Union

74 M Garcia et al A question driven socio-hydrological modeling process

Human and hydrological systems are coupled Many im-

pacts of human activity on the hydrological system are now

well documented (Tong and Chen 2002 Wissmar et al

2004 Voumlroumlsmarty et al 2010 Vahmani and Hogue 2014)

and there is increasing evidence that how and when hu-

mans respond individually and collectively to hydrological

change has important implications for water resources plan-

ning management and policy (Srinivasan et al 2010 Di

Baldassarre et al 2013 Elshafei et al 2014) These obser-

vations have prompted a call to treat humans as an endoge-

nous component of the water cycle (Wagener et al 2010

Sivapalan et al 2012) Representing water systems as cou-

pled humanndashhydrological systems or socio-hydrological sys-

tems with two-way feedback allows new research questions

and potentially transformative insights to emerge

Traditional modeling approaches assume that there is no

feedback between hydrological and human systems and

therefore cannot provide insights into how different patterns

of natural variability or human-induced change may prop-

agate through the coupled system Over short timescales

such as a year many human and hydrological variables

can be considered constant and their couplings may be ig-

nored (Srinivasan 2015) However water resources infras-

tructure decisions have impacts on longer (decadal to cen-

tury) timescales therefore there is a need for an approach

that can handle not only long-term variability and nonsta-

tionarity in the driving variables (eg precipitation temper-

ature population) but also addresses how these changes can

propagate through the coupled system affecting the struc-

ture and properties of the coupled system (Sivapalan et al

2012 Thompson et al 2013) Dynamic modeling of socio-

hydrological systems recognizes the potential for humans to

transform hydrological systems and for hydrological condi-

tions to influence human behavior While human behavior

is usually incorporated into a model through scenarios sce-

narios cannot include two-way feedback Building effects of

human behavior into a simulation model can enable testing

of feedback cycles and can illuminate the impact of feed-

back and path dependencies that are not easily identifiable in

scenario-based modeling

Coupled modeling on the other hand introduces new

challenges First it is not possible to exhaustively model

complex systems such as the coupled humanndashhydrological

system (Sterman 2000 Schluumlter et al 2014) Bounds must

be set to develop an effective model but researchers are chal-

lenged to objectively define the scope of coupled modeling

studies Second by definition coupled models cross disci-

plines and modelers are unable to point to the theoretical

framework of any single discipline to defend the relevant

scope (Srinivasan 2015) At the same time researchers must

balance the scope and level of detail in order to create a

parsimonious and communicable model Finally critical as-

sessment of models is more challenging when the theories

empirical methods and vocabulary drawn upon to create and

communicate a model span disciplinary boundaries (Schluumlter

et al 2014) At the same time critique is needed to move

the field forward as the science is new and lacks established

protocols Transparency of the model aims the development

process conceptual framework and assumptions are thus par-

ticularly important A structured but flexible modeling pro-

cess can address these challenges by encouraging modelers

to clearly define model objectives document reasoning be-

hind choices of scale scope and detail and take a broad view

of potentially influential system processes

In this paper we present a question driven process for mod-

eling socio-hydrological systems that builds on current mod-

eling tools from both domains and allows the flexibility for

exploration We demonstrate this process by revisiting a clas-

sic question in water resources engineering on reservoir op-

eration rules the tradeoff between standard operating policy

(SOP) and hedging policy (HP) Under SOP demand is ful-

filled unless available supply drops below demand under HP

water releases are reduced in anticipation of a deficit to de-

crease the risk a large shortfall (Cancelliere et al 1998) We

add to this classic question a linkage between supply relia-

bility and demand As this question has been asked by nu-

merous researchers before it offers an excellent opportunity

to test the utility of our proposed modeling framework using

a hypothetical municipality called Sunshine City as a case

study

2 Modeling socio-hydrological systems

Modeling the interactions between human and hydrological

systems exacerbates challenges found in modeling purely hy-

drological systems including setting the model boundary de-

termining the relevant processes and relationships and clearly

communicating model framing and assumptions Common

approaches to hydrological modeling are reviewed to put

socio-hydrological modeling in the context of hydrological

modeling practice Next modeling approaches used in sys-

tem dynamics and social-ecological systems science both

of which address coupled systems are described Then

socio-hydrological modeling approaches are reviewed and

gaps identified While no one approach is directly trans-

ferrable to socio-hydrological systems practices from hy-

drological modeling along with those from integrative dis-

ciplines serve as a baseline for comparison and inform our

socio-hydrological modeling process We then present our

recommendations for socio-hydrological model conceptual-

ization

21 Modeling hydrological systems

In hydrology the basic steps of model development are

(a) data collection and analysis (b) conceptual model devel-

opment (c) translation of the conceptual model to a mathe-

matical model (d) model calibration and (e) model valida-

tion (Bloumlschl and Sivapalan 1995) While the basic steps

Hydrol Earth Syst Sci 20 73ndash92 2016 wwwhydrol-earth-syst-scinet20732016

M Garcia et al A question driven socio-hydrological modeling process 75

of model development are generally accepted in practice

approaches diverge particularly in conceptual model de-

velopment In hydrology Wheater et al (1993) identified

four commonly used modeling approaches physics-based

concept-based (also called conceptual) data driven and hy-

brid datandashconceptual Physics-based models represent a sys-

tem by linking small-scale hydrological processes (Sivapalan

et al 2003) Concept-based models use prior knowledge to

specify the influential processes and determine the structure

Data driven models are derived primarily from observations

and do not specify the response mechanism Hybrid datandash

conceptual models use data and prior knowledge to infer

model structure (Wheater et al 1993 Sivapalan et al 2003)

Modeling purpose typically determines the modeling ap-

proach Environmental models may be developed to formu-

late and test theories or to make predictions (Beven 2002)

Physics-based models can be used to test theories about

small-scale processes or to predict catchment response by

scaling up these processes Concept-based models hypoth-

esize the important elements and processes and their struc-

ture of interaction to answer a question or predict a certain

property although hypotheses are often not explicitly stated

and tested (Wheater et al 1993) A reliance on prior knowl-

edge limits the applicability of concept-based modeling in

fields lacking consensus on both the presence and relevance

of feedback processes Data driven models are effective in

prediction While they have potential for hypothesis testing

a focus on black box inputndashoutput models limits insight into

system processes and the ability to extrapolate beyond ob-

served data (Sivapalan et al 2003) Hybrid datandashconceptual

models use data and other knowledge to generate and test

hypotheses about the structure of the system (Wheater et al

1993 Young 2003) As socio-hydrology is a new area of re-

search prior knowledge alone is insufficient and the focus

is on modeling to enhance understanding through hypothesis

generation and testing hybrid datandashconceptual modeling tac-

tics aimed at enhancing understanding therefore inform our

proposed process

22 Modeling coupled systems

While coupling of natural and human systems is in its in-

fancy in hydrology there is a strong tradition of studying

coupled systems in the fields of system dynamics and social-

ecological systems These fields have developed approaches

to understand and model complex systems and can inform

a socio-hydrological modeling process First in both fields

the research question or problem drives modeling decisions

Much of the work to date on socio-hydrological systems is

exploratory and aims to explain evidence of system coupling

seen in case data Developing a model to answer a question

or solve a problem allows a more structured and defensible

framework to support the modeling decisions and provides

a benchmark for model validation (Sterman 2000 Hinkel

et al 2015) For example Jones et al (2002) in modeling

the sawmill industry in the northeastern United States focus

on understanding if the system has the structural potential to

overshoot sustainable yield While the resulting model is a

significant simplification of a complex system the reason for

inclusion of tree growth dynamics mill capacity and lumber

prices and the exclusion of other variables is clear Second

system dynamics and social-ecological systems science use

multiple data sources both quantitative and qualitative to

specify and parameterize model relationships Omitting in-

fluential relationships or decision points due to lack of quan-

titative data results in a greater error than their incorrect spec-

ification (Forrester 1992) Third system dynamics focuses

on developing a dynamic hypothesis that explains the system

behavior of interest in terms of feedback processes (Sterman

2000) Finally social-ecological systems science has found

that the use of frameworks as part of a structured model de-

velopment process can aid transparency and comparability

across models (Schluumlter et al 2014)

23 Progress and gaps in socio-hydrological modeling

Several research teams have operationalized the concepts

of socio-hydrology using approaches ranging from simple

generic models to contextual data-driven models Di Baldas-

sarre et al (2013) developed a simple generic model to ex-

plore the dynamics of humanndashflood interactions for the pur-

pose of showing that human responses to floods can exacer-

bate flooding problems Viglione et al (2014) extended this

work to test the impact of collective memory risk-taking atti-

tude and trust in risk reduction measures on humanndashflood dy-

namics Kandasamy et al (2014) analyzed the past 100 years

of development in the Murrumbidgee River basin in eastern

Australia and built a simple model of the transition from the

dominance of agricultural development goals through a slow

realization of adverse environmental impacts to emergence

of serious ecological restoration efforts Elshafei et al (2014)

proposed a conceptual socio-hydrological model for agricul-

tural catchments and applied it to the Murrumbidgee and the

Lake Toolibin basins they then built upon this conceptual

model to construct a detailed semi-distributed model of the

Lake Toolibin basin (Elshafei et al 2015) Srinivasan and

collaborators analyzed water security in the city of Chennai

India By modeling the feedback between household level

coping mechanisms and regional-scale stressors the team ex-

plained the counterintuitive effects of policy responses such

as the observation that reduced groundwater recharge caused

by fixing leaky pipelines decreased a householdrsquos ability to

use wells to cope with water system interruptions (Srinivasan

et al 2010 2013)

Researchers have also addressed the methodological ques-

tions of how to frame and model socio-hydrological sys-

tems Blair and Buytaert (2015) provide a detailed review

of the model types and modeling methods used in socio-

hydrology and those that may have utility in the field Siva-

palan and Bloumlsch (2015) offer guidance on framing and mod-

wwwhydrol-earth-syst-scinet20732016 Hydrol Earth Syst Sci 20 73ndash92 2016


eling socio-hydrological systems from stating framing as-

sumptions to model validation techniques and highlight the

specific challenges of scale interactions found in these cou-

pled systems Elshafei et al (2014) and Liu et al (2014) de-

tailed the development of conceptual models giving readers

insight into the framing of their case study work

These methodological advances have begun to address the

many challenges of translating the concept of feedback be-

tween human and hydrological systems into actionable sci-

ence However obstacles remain principally expanding the

scope of modeling to include societal systems and human

decision-making exacerbates the challenges of setting the

model boundary and process detail and of evaluating those

choices The source of this challenge is twofold First there

are fundamental differences between natural and social sys-

tems The laws governing physical chemical and biological

systems such as conservation of mass and energy are broadly

applicable across contexts the relevance of rules influenc-

ing social systems varies by context Second the modeling

of coupled humanndashhydrological systems is new intellectual

territory At this intersection the norms and unstated assump-

tions instilled by disciplinary training must be actively ques-

tioned and examined within a transparent model develop-

ment testing and validation process

There are no universally accepted laws of human behavior

as there are for the physical and biological sciences (Loucks

2015) While institutions (formal and informal rules) influ-

ence behavior the impact of institutions on the state of the

system depends on whether people follow the rules (Schlager

and Heikkila 2011) Additionally these rules are not static

In response to outcomes of past decisions or changing con-

ditions actors change both the rules that shape the options

available for practical decisions and the rules governing the

collective choice process through which these operation rules

are made (McGinnis 2011) Furthermore water policy de-

cisions are not made in isolation of other policy decisions

Decisions are interlinked as the same actors may interact

with and get affected differently depending on the contexts

(McGinnis 2011b) The outcome of a related policy deci-

sion may alter the choices available to actors or the resources

available to address the current problem The state of the hy-

drological system particularly during extreme events can

spark institutional changes yet other factors such as polit-

ical support and financial resources as well as the prepared-

ness of policy entrepreneurs also play a role (Crow 2010

Hughes et al 2013) Given this complexity Pahl-Wostl et

al (2007) argue that recognizing the unpredictability of pol-

icy making and social learning would greatly improve the

conceptualization of water management Nevertheless some

dynamics persist across time and space water management

regimes persist for decades or centuries and some transitions

in different locations share characteristics (Elshafei et al

2014 Kandasamy et al 2014 Liu et al 2014) Furthermore

modeling is a useful tool to gain insight into the impacts

of these dynamics (Thompson et al 2013 Sivapalan and

Bloumlschl 2015) However complex systems such as socio-

hydrological systems cannot be modeled exhaustively (Ster-

man 2000 Schluumlter et al 2014) Rather model conceptu-

alization must balance sufficient process representation and

parsimony (Young et al 1996 Ostrom 2007)

Model conceptualization is based on general assumptions

about how a system works Often these assumptions are im-

plicit and not challenged by others within the same research

community (Kuhn 1996) This works well when research

stays within the bounds of the existing methods theories

and goals of onersquos research community when working in

new intellectual territory research community norms can-

not be relied upon to guide assumptions Further disciplinary

training is highly successful at teaching these community

norms and researchers working on interdisciplinary projects

must actively question the framing assumptions they bring

to the project (Leacuteleacute and Norgaard 2005 McConnell et al

2009) By its integrative nature socio-hydrological model-

ing crosses disciplines and modelers are unable to point to

the theoretical framework of any single discipline to make

simplifying assumptions (Srinivasan 2015) In absence of

research community norms we must return to modeling fun-

damentals Models are simplifications of real systems that

in a strict sense cannot be validated but the acceptability of

model assumptions for the question at hand can be assessed

(Sterman 2000) Careful articulation of the research ques-

tions links the assessment of important variables and mech-

anisms to the question context This allows the critique to

focus on the acceptability of these choices relative to model

goals and enables critical assessment of the range of appli-

cability of identified processes through case and model com-

parison

The recent Water Resources Research Debate Series of-

fers an excellent illustration of this point Di Baldassarre

et al (2015) catalyze the debate by presenting a generic

model of humanndashflood interaction This model incorporates

both the ldquolevee effectrdquo in which periods of infrequent flood-

ing (sometimes caused by flood protection infrastructure) in-

crease the tendency for people to settle in the floodplain and

the ldquoadaptation effectrdquo in which the occurrence of flooding

leads to an adaptive response In the model they link flood

frequency and adaptive action through a social memory vari-

able which increases with the occurrence of floods and de-

cays slowly overtime flood occurrence directly triggers levee

heightening in technological societies and indirectly through

the social memory decreases floodplain population density

(Di Baldassarre et al 2015)

In the debate this modeling approach is both commended

as an impressive innovation and critiqued for its simpli-

fication of social dynamics (Gober and Wheater 2015

Loucks 2015 Sivapalan 2015 Troy et al 2015) Gober and

Wheater (2015) note that while social or collective memory

is an important factor in flood resilience it does not determine

flood response flood awareness may or may not result in an

adaptive response based on the way individuals the media



and institutions process the flood threat the social capacity

for adaptation and the preparedness of policy entrepreneurs

among other factors Loucks (2015) observes that data on

past behavior is not necessarily an indicator of future be-

havior and suggests that observing stakeholder responses to

simulated water management situations may offer additional

insight Troy et al (2015) and Di Baldassarre et al (2015)

note that the humanndashflood interaction model presented rep-

resents a hypothesis of system dynamics which allows for

exploration and that simple stylized models enable gener-

alization across space and time In sum the debate presents

different perspectives on the acceptability of the modeling

assumptions

A close look at how the debate authors critique and

commend the humanndashflood interaction model illustrates

that the acceptability of modeling assumptions hinges

upon the modelrsquos intended use For example Gober and

Wheater (2015) critique the simplicity of social memory as a

proxy for social system dynamics but acknowledge the util-

ity of the model in clarifying the tradeoffs of different ap-

proaches to meet water management goals As we can never

have comprehensive representation of a complex and cou-

pled humanndashhydrological system we need transparency of

the abstracting assumptions and their motivation This is not

a new insight however a question driven modeling process

allows the flexibility and transparency needed to examine the

acceptability of model assumptions while acknowledging the

role of context and the potential for surprise

24 A question driven modeling process

Our proposed process begins with a research question The

research question is then used to identify the key outcome

metric(s) A dynamic hypothesis is developed to explain the

behavior of the outcome metric over time a framework can

be used to guide and communicate the development of the

dynamic hypothesis Remaining model processes are then

specified according to established theory

As emphasized by both system dynamics and social-

ecological systems researchers the research question drives

the process of system abstraction One way to think about

this process of abstraction is through the lens of forward

and backward reasoning Schluumlter et al (2014) introduced

the idea of forward and backward reasoning to develop con-

ceptual models of social-ecological systems In a backward-

reasoning approach the question is first used to identify in-

dicators or outcome metrics next the analysis proceeds to

identify the relevant processes and then the variables and

their relationships as seen in Fig 1 (Schuumllter et al 2014)

These three pieces then form the basis for the conceptual

model In contrast a forward-reasoning approach begins

with the identification of variables and relationships and then

proceeds toward outcomes Forward reasoning is most suc-

cessful when there is expert knowledge of the system and

backward-reasoning is useful primarily when prior knowl-

RESEARCH QUESTION

CONCEPTUAL MODEL

VARIABLES amp RELATIONSHIPS

PROCESSES

OUTCOME INDICATORS BACK

WAR

D RE

ASO

NIN

G

PROCESSES


OUTCOME INDICATORS

FORW

ARD

REAS

ON

ING

Figure 1 Backward-reasoning process (adapted from Schluumlter et

al 2014)

edge is insufficient (Arocha et al 1993) As few researchers

have expert knowledge of all domains involved in socio-

hydrological modeling and data is often sparse a backward-

reasoning approach is here used to conceptualize a socio-

hydrological model Additionally this outcome-oriented ap-

proach will focus the scope of the model on the questionrsquos

relevant variables and processes

The research question helps to define the outcome met-

ric(s) of interest however determining the relevant processes

and variables requires further analysis One tool to identify

influential processes and variables is the dynamic hypothe-

sis A dynamic hypothesis is a working theory informed by

data of how the system behavior in question arose (Sterman

2000) It is dynamic in nature because it explains changes

in behavior over time in terms of the structure of the system

(Stave 2003) The dynamic hypothesis could encompass the

entire socio-hydrological model but in practice many pro-

cesses within a model will be based on established theory

such as rainfall runoff or evaporation processes The intent is

to focus the dynamic hypothesis on a novel theory explaining

observed behavior Stating the dynamic hypothesis clarifies

which portion of the model is being tested

A framework can aid the development of the dynamic hy-

potheses and the communication of the reasoning behind

it The use of frameworks enhances the transparency of

model development by clearly communicating the modelerrsquos

broad understanding of a system Socio-hydrological model-

ers can develop their own framework (Elshafei et al 2014)

or draw on existing frameworks that address coupled humanndash

hydrological systems such as the social-ecological systems

(SES) framework the management transition framework

or the integrated structurendashactorndashwater framework (Ostrom

2007 Pahl-Wostl et al 2010 Hale et al 2015)

To illustrate how a framework may be used in model con-

ceptualization we will focus on the SES framework The SES



framework is a nested conceptual map that partitions the at-

tributes of a social-ecological system into four broad classes

(1) resource system (2) resource units (3) actors and (4) the

governance system (McGinnis and Ostrom 2014) Each of

the four top tier variables has a series of second tier (and po-

tentially higher tier) variables for example storage charac-

teristics and equilibrium properties are second tier attributes

of the resource system (Ostrom 2009) The SES framework

prescribes a set of elements and general relationships to con-

sider when studying coupled social and ecological systems

(Ostrom 2011) The variables defined in the SES frame-

work were found to impact the interactions and outcomes of

social-ecological systems in a wide range of empirical stud-

ies (Ostrom 2007) In addition to specifying candidate vari-

ables the SES framework specifies broad process relation-

ships (Schluumlter et al 2014) At the broadest level SES spec-

ifies that the state of the resource system governance system

resource unit properties and actor characteristics influence

interactions and are subsequently influenced by the outcomes

of those interactions To operationalize the SES framework

for model conceptualization one must move down a level

to assess the relevance of the tier two variables against case

data and background knowledge This review aims to check

the dynamic hypothesis against a broader view of coupled

system dynamics and to inform determination of remaining

model processes

The following case presents the development of a socio-

hydrological (coupled) and a traditional (noncoupled) model

to illustrate this process While this process is developed to

study real-world cases a hypothetical case is used here for

simplicity brevity and proof of concept

3 Sunshine City a case study of reservoir operations

Sunshine City is located in a growing region in a semi-arid

climate The region is politically stable technologically de-

veloped with a market economy governed by a representa-

tive democracy Sunshine City draws its water supply from

the Blue River a large river which it shares with downstream

neighbors The water users must maintain a minimum flow

in the Blue River for ecological health Sunshine City can

draw up to 25 of the annual flow of the Blue River in any

given year A simple prediction of the yearrsquos flow is made by

assuming that the flow will be equal to the previous yearrsquos

flow the resulting errors are corrected by adjusting the next

yearrsquos withdrawal

The cityrsquos Water Utility is responsible for diverting treat-

ing and transporting water to city residents and businesses

It is also tasked with making infrastructure investment deci-

sions setting water prices Water users receive plentiful sup-

ply at cost and there have been no shortages in recent years

While located in a semi-arid environment the large size of

Sunshine Cityrsquos Blue River water availability and allocation

created a comfortable buffer The cityrsquos Water Utility is also

Table 1 Summary of Sunshine City properties

Sunshine City properties

Variable Value Units

Blue River mean flow 2 km3 yrminus1

Blue River variance 05 km3 yrminus1

Blue River lag 1 autocorrelation 06 ndash

Average evaporation rate 1 m yrminus1

Population 1 000 000 people

Average annual growth rate 3

Per capita water usage 400 m3 yrminus1

Water price 025 USD mminus3

Reservoir capacity 02 km3

Reservoir slope 01 ndash

responsible for setting water efficiency codes and other con-

servation rules The current building code includes only basic

efficiencies required by the national government The Blue

River along with other regional sources is fully allocated

making future augmentation of supplies unlikely See Table 1

above for a summary of key characteristics of Sunshine City

Along with the rest of the region Sunshine Cityrsquos popula-

tion and its water demand has grown rapidly over the past

few years Managers at the Water Utility are concerned they

will no longer be able to meet its reliability targets as de-

mands rise and have added a reservoir to increase future re-

liability They now must decide how to operate the reservoir

and are considering two options standard operating policy

(SOP) and hedging policy (HP) The selected operating pol-

icy must satisfy downstream user rights and maintain min-

imum ecological flows In addition to meeting the legal re-

quirements the Water Utility managers are concerned with

finding a policy that will enable the city to provide the most

reliable water supply throughout the lifetime of the reservoir

(50ndash100 years) From experience they have observed that

both water price and reliability affect demand A key puz-

zle that emerges for water managers from this experience is

how do operational rules governing use of water storage in-

fluence long-term water supply reliability when consumers

make water usage decisions based on both price and relia-

bility

As the question implies the Water Utility managers have

a working hypothesis relating demand change with water

shortages Therefore along with the research question the

following dynamic hypothesis is considered the occurrence

of water shortages increases the tendency of users to adopt

water conservation technologies and to make long-term be-

havioral changes HP triggers shortages sooner than SOP

thus triggering earlier decreases in demand


M Garcia et al A question driven socio-hydrological modeling process 79RE

LEAS

E

STORAGE AT THE END OF PREVIOUS PERIOD PLUS PREDICTED INFLOW

DP

DP VMAX + DP

1

1

1

1

Figure 2 Standard operating policy whereD is per capita demand

P is population and Vmax is reservoir capacity (adapted from Shih

and ReVelle 1994)

31 Background

The decision of how much water to release for use each time

period is deceptively complex due to the uncertainty of fu-

ture streamflows and the nonlinear benefits of released water

(Shih and ReVelle 1994 Draper and Lund 2004) In mak-

ing release decisions water utilities must fulfill their man-

date to maintain a reliable water supply in a fiscally efficient

manner Reliability is the probability that the system is in

a satisfactory state (Hashimoto et al 1982) In this case a

satisfactory system state is one in which all demands on the

system can be met The definition of an unsatisfactory state

is more nuanced Water shortages have a number of charac-

teristics that are important to water management including

frequency maximum shortage in a given time period and

length of shortage period (Cancelliere et al 1998) Long-

term reliability here refers to the projected reliability over

several decades The time frame used for long-term projec-

tions varies between locations and utilities (ie Boston uses

a 25-year time frame Denver uses a 40-year time frame and

Las Vegas uses a 50-year time frame) and a 50-year time

frame is used here (MWRA 2003 SNWA 2009 Denver

Water 2015)

Two operational policies SOP and HP are commonly used

to address this decision problem Under SOP demand is al-

ways fulfilled unless available supply drops below demand

under HP water releases are limited in anticipation of an ex-

pected deficit (Cancelliere et al 1998) Hedging is used as

a way to decrease the risk of a large shortfall by imposing

conservation while stored water remains available Figures 2

and 3 illustrate SOP and HP respectively For this simple ex-

periment only linear hedging where KP is the slope of the

release function is tested

The traditional argument for hedging is that it is economi-

cal to allow a small deficit in the current time period in order

to decrease the probability of a more severe shortage in a fu-

ture time periods (Bower et al 1962) This argument holds

true if the loss function associated with a water shortage is

RELE

ASE


DP

KPDP VMAX + DP

KP

1

1

1

Figure 3 Hedging policy where KP is hedging release function

slope (adapted from Shih and ReVelle 1994)

nonlinear and convex in other words that a severe shortage

has a larger impact than the sum of several smaller short-

ages (Shih and ReVelle 1994) Gal (1979) showed that the

water shortage loss function is convex thereby proving the

utility of hedging as a drought management strategy Other

researchers have shown that hedging effectively reduces the

maximum magnitude of water shortages and increases total

utility over time (Shih and ReVelle 1994 Cancelliere et al

1998) More recent work by Draper and Lund (2004) and

You and Cai (2008) confirms previous findings and demon-

strates the continued relevance reservoir operation policy se-

lection

Researchers and water system managers have for decades

sought improved policies for reservoir operation during

drought periods (Bower et al 1962 Shih and ReVelle 1994

You and Cai 2008) We add to this classic question the ob-

servation that water shortages influence both household con-

servation technology adoption rates and water use behav-

ior In agreement with Giacomoni et al (2013) we hypoth-

esize that the occurrence of water shortages increases the

tendency of users to adopt water conservation technologies

and to make long-term behavioral changes Household water

conservation technologies include low flow faucets shower

heads and toilets climatically appropriate landscaping grey

water recycling and rainwater harvesting systems (Schuetze

and Santiago-Fandintildeo 2013) The adoption rates of these

technologies are influenced by a number of factors includ-

ing price incentive programs education campaigns and peer

adoption (Campbell et al 2004 Kenney et al 2008) A re-

view of studies in the US Australia and UK showed that

the installation of conservation technologies results in indoor

water savings of 9ndash12 for fixture retrofits and 35ndash50

for comprehensive appliance replacements (Inman and Jef-

frey 2006) In some cases offsetting behavior reduces these

potential gains however even with offsetting the adoption

of conservation technologies still results in lower per capita

demands (Geller et al 1983 Fielding et al 2012) Wa-

ter use behavior encompasses the choices that individuals

make related to water use ranging from length of showers



Table 2 Household conservation action by shortage experience

(ISTPP 2013)

Last experienced Percent of households over the

a water shortage past year that have

invested in changed taken

efficient fixtures water use no

or landscapes behavior action

Within a year 56 88 11

1ndash2 years ago 52 87 11



10 or more years ago 42 74 24

Never experienced 36 66 31

and frequency of running the dishwasher to timing of lawn

watering and frequency of car washing Water use behavior

is shaped by knowledge of the water system awareness of

conservation options and their effectiveness and consumerrsquos

attitudes toward conservation (Frick et al 2004 Willis et

al 2011) Changes to water use behavior can be prompted

by price increases education campaigns conservation reg-

ulations and weather (Campbell et al 2004 Kenney et al

2008 Olsmtead and Stavins 2009)

As a city begins to experience a water shortage the wa-

ter utility may implement water restrictions price increases

incentive programs or education campaigns to influence con-

sumer behavior While staff within the water utility or city

may have planned these measures before the occurrence of

a water shortage event particularly if it aligns with other

driving forces offers a window of opportunity to implement

sustainable water management practices (Jones and Baum-

gartner 2005 Hughes et al 2013) In addition water users

are more likely to respond to these measures with changes

in their water use behavior andor adoption of conservation

technologies during shortages Baldassare and Katz (1992)

examined the relationship between the perception of risk to

personal well-being from an environmental threat and adop-

tion of environmental practices with a personal cost (finan-

cial or otherwise) They found that the perceived level of en-

vironmental threat is a better predictor for individual envi-

ronmental action including water conservation than demo-

graphic variables or political factors Illustrating this effect

Mankad and Tapsuwan (2011) found that adoption of alterna-

tive water technologies such as on-site treatment and reuse

is increased by the perception of risk from water scarcity

Evidence of individual level behavior change can also be

seen in the results of a 2013 national water policy survey con-

ducted by the Institute for Science Technology and Public

Policy at Texas AampM University The survey sampled over

3000 adults from across the United States about their atti-

tudes and actions related to a variety of water resources and

public policy issues Included in the survey were questions

that asked respondents how recently if ever they person-

ally experienced a water shortage and which if any house-

hold efficiency upgrade or behavioral change actions their

household had taken in the past year Efficiency upgrade op-

tions offered included low-flow shower heads low-flush toi-

lets and changes to landscaping behavioral options given in-

cluded shorter showers less frequent dishwasher or wash-

ing machine use less frequent car washing and changes to

yard watering (ISTPP 2013) As seen in Table 2 respon-

dents who had recently experienced a water shortage were

more likely to have made efficiency investments and to have

changed their water use behavior This finding is corrobo-

rated by a recent survey of Colorado residents Of the 72 of

respondents reporting increased attention to water issues the

most-cited reason for the increase (26 of respondents) was

a recent drought or dry year (BBC Research 2013) Other

reasons cited by an additional 25 of respondents including

news coverage water quantity issues and population growth

may also be related water shortage concerns or experiences

The increased receptivity of the public to water conserva-

tion measures and the increased willingness of water users

to go along with these measures during shortage events com-

bine to drive changes in per capita demands The combined

effect of these two drivers was demonstrated in a study

of the Arlington Texas water supply system (Giacomoni

et al 2013 Kanta and Zechman 2014) Additional exam-

ples of city- and regional-scale drought response leading to

long-term demand decreases include the droughts of 1987ndash

1991 and the mid-2000s in California and of 1982ndash1983 and

1997ndash2009 in Australia (Zilberman et al 1992 Turral 1998

Sivapalan et al 2012 Hughes et al 2013) It is often dif-

ficult to separate the relative effects of the multiple price

and nonprice approaches applied by water utilities during

droughts (Olmstead and Stavins 2009) The point is how-

ever that the response generally points to lower per capita

water demands

One example of lasting water use reductions after a short-

age is the 1987ndash1992 drought in Los Angeles California An

extensive public awareness and education campaign sparked

both behavioral changes and the adoption of efficient fixtures

such as low-flow shower heads and toilets and increasing

block pricing introduced after the drought helped maintain

conservation gains (LADWP 2010) Evidence of the lasting

effect can be seen in Fig 4 Per capita water demands do not

return to 1990 levels after the drought ends in 1992 Note that

the data below also contains a counter example The 1976ndash

1977 drought caused a sharp drop in water consumption in

Los Angeles however consumption quickly returned to pre-

drought levels when the rainfall returned in 1978 While the

1976ndash1977 drought was more intense than any year in the

1987ndash1992 drought the long duration of the later drought

caused deeper draw downs in the cityrsquos water reserves ul-

timately prompting transformative action (LADWP 2010)

This may indicate that the impact of the 1976ndash1977 drought

was below the threshold for significant action or that other

priorities dominated public attention and resources at the



0

50

100

150

200

1970 1980 1990 2000 2010Year

Per

cap

ita d

eman

d (g

allo

ns p

er d

ay)

Figure 4 Historical city of Los Angeles water use (LADWP 2010)

time In sum the Los Angeles case serves both to illustrate

that hydrological change can prompt long-term changes in

water demands and as a reminder that multiple factors influ-

ence water demands and hydrological events will not always

dominate

32 Model development

The Sunshine City water managers want to understand how

the operational rules governing use of water storage influence

long-term water supply reliability when consumers make wa-

ter usage decisions based on price and reliability A model

can help the managers gain insight into systemrsquos behavior

by computing the consequences of reservoir operation pol-

icy choice over time and under different conditions As de-

scribed in the background section many supply side and de-

mand side factors affect water system reliability However

not all variables and processes are relevant for a given ques-

tion A question driven modeling process uses the question to

determine model boundary and scope rather than beginning

with a prior understanding of the important variables and pro-

cesses A question driven process is here used to determine

the appropriate level of system abstraction for the Sunshine

City reservoir operations model

From the research question it is clear that reliability is the

outcome metric of interest and that the model must test for

the hypothesized link between demand changes and reliabil-

ity Reliability as defined above is the percent of time that all

demands can be met The SES framework is used to guide the

selection of processes and variables including the dynamic

hypothesis Given this wide range the framework was then

compared against the variables and processes found to be in-

fluential in urban water management and socio-hydrological

studies (Brezonik and Stadelmann 2002 Abrishamchi et al

2005 Padowski and Jawitz 2012 Srinivasan et al 2013

Dawadi and Ahmad 2013 Elshafei et al 2014 Gober et al

2014 Liu et al 2014 Pande et al 2013 van Emmerik et

al 2014) Based on this evaluation two second tier variables

were added to the framework land use to the resource system

characteristics and water demand to interactions other vari-

ables were modified to reflect the language typically used

in the water sciences (ie supply in place of harvesting)

See Table 3 for urban water specific modification of the SES

framework

We then assess the relevance of the tier two variables

against case data and background knowledge (summarized

in Sects 3 and 31 respectively) by beginning with the out-

come metric reliability Within the framework reliability is

an outcome variable specifically a social performance met-

ric and it is the direct result of water supply and water de-

mand interaction processes Water supply encompasses the

set of utility level decisions on reservoir withdrawals and

discharges As detailed in the case description these deci-

sions are shaped by the selected reservoir operating policy

streamflow the existing environmental flow and downstream

allocation requirements reservoir capacity water in storage

and water demands Streamflow is a stochastic process that

is a function of many climatic hydraulic and land surface

parameters However given the driving question and the as-

sumption that the city represents only a small portion of the

overall watershed a simple statistical representation is suffi-

cient and streamflow is assumed independent of other model

variables

Total water demand is a function of both population and

per capita demand As described in the background section

per capita water demand changes over time in response to

household level decisions to adopt more water efficient tech-

nologies and water use behavior change made by individuals

in each time interval these decisions may be influenced by

conservation policies As conditions change water users re-

assess the situation and if they choose to act decide between

available options such as investment in efficient technology

changing water use behavior and in extreme cases reloca-

tion Therefore per capita demand is a function of price and

historic water reliability as well as available technologies

and water userrsquos perception of the water system Since the

focus of the question is on system wide reliability individ-

ual level decisions can be modeled in the aggregate as to-

tal demand which is also influenced by population Popu-

lation increases in proportion to the current population as

regional economic growth is the predominant driver of mi-

gration trends However in extreme cases perceptions of re-

source limitations can also influence growth rates The SES

variables used in the conceptual model are highlighted in Ta-

ble 3 and the resulting processes are summarized in Fig 5

Only a subset of the variables and processes articulated in

the SES framework are included in the conceptual model

other variables and processes were considered but not in-

cluded For example economic development drives increas-

ing per capita water demands in many developing regions

but the relationship between economic growth and water de-

mands in highly developed regions is weaker due to the in-

creased cost of supply expansion and greater pressure for

environmental protection (Gleick 2000) The income elas-



Table 3 SES framework modified for urban water systems

First tier variables Second tier variables Third tier variables (examples)

Socio economic S1 ndash Economic development Per capita income

and political settings S2 ndash Demographic trends Rapid growth

S3 ndash Political stability Frequency of government turnover

S4 ndash Other governance systems Related regulations

S5 ndash Markets Regional water markets

S6 ndash Media organizations Media diversity

S7 ndash Technology Infrastructure communications

Resource systems1 RS1 ndash Type of water resource Surface water groundwater

RS2 ndash Clarity of system boundaries Groundwaterndashsurface water interactions

RS3 ndash Size of resource system Watershed or aquifer size

RS4 ndash Human-constructed facilities Type capacity condition

RS5 ndash Catchment land use Urbanization reforestation

RS6 ndash Equilibrium properties Mean streamflow sustainable yield

RS7 ndash Predictability of system dynamics Data availability historic variability

RS8 ndash Storage characteristics Naturalbuilt volume

RS9 ndash Location

Governance systems2 GS1 ndash Government organizations Public utilities regulatory agencies

GS2 ndash Nongovernment organizations Advocacy groups private utilities

GS3 ndash Network structure Hierarchy of organizations

GS4 ndash Water-rights systems Prior appropriation beneficial use

GS5 ndash Operational-choice rules Water use restrictions operator protocol

GS6 ndash Collective-choice rules Deliberation rules position rules

GS7 ndash Constitutional-choice rules Boundary rules scope rules

GS8 ndash Monitoring and sanctioning rules Enforcement responsibility

Resource units3 RU1 ndash Interbasin connectivity Infrastructure surfacendashgroundwater interactions

RU2 ndash Economic value Water pricing presence of markets

RU3 ndash Quantity Volume in storage current flow rate

RU4 ndash Distinctive characteristics Water quality potential for public health impacts

RU5 ndash Spatial and temporal distribution Seasonal cycles interannual cycles

Actors A1 ndash Number of relevant actors

A2 ndash Socioeconomic attributes Education level income ethnicity

A3 ndash History or past experiences Extreme events government intervention

A4 ndash Location

A5 ndash Leadershipentrepreneurship Presence of strong leadership

A6 ndash Norms (trust-reciprocity)social capital Trust in local government

A7 ndash Knowledge of SESmental models Memory mental models

A8 ndash Importance of resource (dependence) Availability of alternative sources

A9 ndash Technologies available Communication technologies efficiency technologies

A10 ndash Values Preservation of cultural practices

Action situations I1 ndash Water supply Withdrawal transport treatment distribution

interactionsrarr outcomes4 I2 ndash Information sharing Public meetings word of mouth

I3 ndash Deliberation processes Ballot initiatives board votes public meetings

I4 ndash Conflicts Resource allocation conflicts payment conflicts

I5 ndash Investment activities Infrastructure construction conservation technology

I6 ndash Lobbying activities Contacting representatives

I7 ndash Self-organizing activities Formation of NGOs

I8 ndash Networking activities Online forums

I9 ndash Monitoring activities Sampling Inspections self-policing

I10 ndash Water demand IndoorOutdoor residentialcommercialindustrial

O1 ndash Social performance measures Efficiency equity accountability

O2 ndash Ecological performance measures Sustainability minimum flows

O3 ndash Externalities to other SESs Ecosystem impacts

Related ecosystems ECO1 ndash Climate patterns El Nintildeo impacts climate change projections

ECO2 ndash Pollution patterns Urban runoff upstream discharges

ECO3 ndash Flows into and out of focal SES Upstream impacts downstream rights

Note variables added are in italic variables key to the conceptual model are in bold Examples of third tier variables are given for clarification 1 Resource system variables

removed or replaced productivity of system 2 Governance system variables removed or replaced property 3 Resource unit variables removed or replaced resource unit

mobility growth or replacement rate interaction among resource units number of units 4 Interaction and outcome variables removed or replaced harvesting



Reservoir storage

Shortageawareness

Waterdemand

Water supply

Water shortage

+

-

+

-

-

-

Reservoirstorage

Shortageawareness

Water demand Water supply

Water shortage

+

-

+

-

-

Population

-

+ Growth Rate+Population

+

+

Figure 5 Causal loop diagrams (a) water demand shortage and conservation (b) water demand shortage and population (c) population

and growth rate

Table 4 State and exogenous model variables

Variable Description Units Equation Variable Type

Q Streamflow km3 yrminus1 1 Exogenous

V Reservoir storage volume km3 2 State

P Population Persons 3 State

W Withdrawal km3 yrminus1 4 State

S Shortage magnitude km3 yrminus1 5 State

M Shortage awareness 6 State

D Per capita demand m3 yrminus1 7 State

ticity of water can lead to increased water demands if rates

do not change proportionally (Dalhuisen et al 2003) here

prices are assumed to keep pace with inflation Given this

assumption and the focus on a city in a developed region

economic development likely plays a minor role Similarly

group decision-making and planning processes such as pub-

lic forums voting and elections can shape the responses to

reliability changes over time This model aims to answer a

question about the impact of a policy not the ease or like-

lihood of its implementation Once the policy is established

through whatever process that is used the question here fo-

cuses on its efficacy Therefore group decision-making pro-

cesses need not be included

In addition to determining the appropriate level of detail

of the conceptual model we must determine which variables

change in response to forces outside the model scope (exoge-

nous variables) which variables must be modeled endoge-

nously (state variables) and which can be considered con-

stants (parameters) Again the nature of the question along

with the temporal and spatial scale informs these distinctions

Variables such as stored water volume per capita water de-

mand and shortage awareness will clearly change over the

50-year study period The population of the city is also ex-

pected to change over the study period Under average hy-

drological conditions the population growth rate is expected

to be driven predominately by regional economic forces ex-

ogenous to the system however under extreme conditions

water supply reliability can influence the growth rate There-

fore population is considered a state variable Streamflow

characteristics may change over the 50-year timescale in re-

sponse to watershed wide land use changes and global-scale

climatic changes Streamflow properties are first considered

stationary parameters in order to understand the impact of the

selected operating policy in isolation from land use and cli-

mate change Climate scenarios or feedbacks between popu-

lation and land use can be introduced in future applications of

the model to test their impact on system performance Reser-

voir operating policy summarized as the hedging slope KP

is considered a parameter in the model Alternate values of

parameter KP are tested but held constant during the study

period to understand the long-term impacts of selecting a

given policy Reservoir properties such as capacity and slope

are also held constant to hone in on the effect of operating

policy See Tables 4 and 5 for a summary of variable types

From these model relationships general equations are devel-

oped by drawing from established theory empirical findings

and working hypotheses

Streamflow Q is modeled using a first-order autoregres-

sive model parameterized by mean (microH km3 yrminus1) standard

deviation (σH km3 yrminus1) and lag one autocorrelation (ρH)

The final term at is a normally distributed random variable

with a mean zero and a standard deviation of 1

Qt = ρH (Qtminus1minusmicroH)+ σH

(1minusp2

H

)05

at +microH (1)

At each time step the amount of water in storage V in the

reservoir is specified by a water balance equation where W

is water withdrawal (km3) ηH (km yrminus1) is evaporation A is

area (km2)QD (km3) is downstream demand andQE (km3)



Table 5 Model parameters

Parameters Description Value Units Equation

microH Mean streamflow 20 km3 yrminus1 1

σH Standard deviation of streamflow 05 km3 yrminus1 1

ρH Streamflow lag one autocorrelation 06 ndash 1

ηH Evaporation rate 0001 km yrminus1 2

QD Downstream allocation 050Q km3 2

QE Required environmental flow 025Q km3 2

σT Average slope of reservoir 01 ndash Stagendashstorage curve

δI Regional birth rate 004 yrminus1 3

δE Regional death rate 003 yrminus1 3

δI Regional immigration rate 005 yrminus1 3

δE Regional emigration rate 003 yrminus1 3

τP Threshold 04 ndash 3

Vmax Reservoir capacity 20 km3 4

KP Hedging slope Variable ndash 5

microS Awareness loss rate 005 yrminus1 6

αD Fractional efficiency adoption rate 015 ndash 7

βD Background efficiency rate 00001 ndash 7

DMIN Minimum water demand 200 m3 yrminus1 7

is the required environmental flow

dV

dt=Qt minusWt minus ηHAt minusQDminusQE (2)

Population is the predominant driver of demand in the

model Population (P ) changes according to average birth

(δB yrminus1) death (δD yrminus1) emigration (δE yrminus1) and immi-

gration (δI yrminus1) rates However immigration is dampened

and emigration accelerated by high values of perceived short-

age risk as would be expected at extreme levels of resource

uncertainty (Sterman 2000) The logistic growth equation

which simulates the slowing of growth as the resource car-

rying capacity of the system is approached serves as the ba-

sis for the population function While the logistic function

is commonly used to model resource-constrained population

growth the direct application of this function would be in-

appropriate for two reasons First an urban water system is

an open system resources are imported into the system at a

cost and people enter and exit the system in response to re-

ductions in reliability and other motivating factors Second

individuals making migration decisions may not be aware

of incremental changes in water shortage risk rather per-

ceptions of water stress drive the damping effect on net mi-

gration Finally only at high levels does shortage perception

influence population dynamics To capture the effect of the

open system logistic damping is applied only to immigration

driven population changes when shortage perception crosses

a threshold τP To account for the perception impact the

shortage awareness variable M is used in place of the ratio

of population to carrying capacity typically used this modi-

fication links the damping effect to perceived shortage risk

dP

dt=

Pt [δBminus δD+ δIminus δE]Pt [(δBminus δD)+ δI(1minusMt )minus δE(Mt )] for Mt ge τP

(3)

Water withdrawals W are determined by the reservoir

operating policy in use As there is only one source water

withdrawn is equivalent to the quantity supplied The pre-

dicted streamflow for the coming year is 025timesQtminus1 ac-

counting for both downstream demands and environmental

flow requirements Under SOPKP is equal to one which sets

withdrawals equal to total demand DP (per capita demand

multiplied by population) unless the stored water is insuf-

ficient to meet demands Under HP withdrawals are slowly

decreased once a pre-determined threshold KPDP has been

passed For both policies excess water is spilled when stored

water exceeds capacity Vmax

Wt = (4)Vt + 025Qtminus1minusVmax for Vt + 025Qtminus1 ge

DtPt +Vmax

DtPt for DtPt +Vmax gtVt + 025Qtminus1 geKPDtPt

Vt + 025Qtminus1

KP

for KPDtPt gt Vt + 025Qtminus1

When the water withdrawal is less than the quantity de-

manded by the users a shortage S occurs

St =

DtPt minusWt for DtPt gtWt

0 otherwise(5)

Di Baldassarre et al (2013) observed that in flood plain

dynamics awareness of flood risk peaks after a flood event

This model extends that observation to link water shortage



events to the awareness of shortage risk The first term in

the equation is the shortage impact which is a convex func-

tion of the shortage volume The economic utility of hedging

hinges on the assumption that the least costly options to man-

age demand will be undertaken first As both water utilities

and water users have a variety of demand management and

conservation options available and both tend to use options

from most to least cost-effective a convex shortage loss is

also applicable to the water users (Draper and Lund 2004) It

is here assumed that the contribution of an event to shortage

awareness is proportional to the shortage cost At high levels

of perceived shortage risk only a large shortage will lead to

a significant increase in perceived risk The adaptation cost

is multiplied by one minus the current shortage awareness to

account for this effect The second term in the equation in-

corporates the decay of shortage microS (yrminus1) awareness and

its relevance to decision making that occurs over time (Di

Baldassarre et al 2013)

dM

dt=

(St

DtPt

)2

(1minusMt )minusmicroSMt (6)

Historically in developed regions per capita water de-

mands have decreased over time as technology improved and

as water use practices have changed As described above this

decrease is not constant but rather is accelerated by shocks to

the system To capture this effect there are two portions to

the demand change equation shock-stimulated logistic de-

cay with a maximum rate of α (yrminus1) and a background de-

cay rate β (yrminus1) Per capita water demand decrease acceler-

ates in a time interval if water users are motivated by recent

personal experience with water shortage (ie Mgt0) As a

certain amount of water is required for basic health and hy-

giene there is ultimately a floor to water efficiencies speci-

fied here as Dmin (km3 yrminus1) Reductions in per capita water

usage become more challenging as this floor is approached a

logistic decay function is used to capture this effect When no

recent shortages have occurred (ie M = 0) there is still a

slow decrease in per capita water demands This background

rate β of demand decrease is driven by both the replacement

of obsolete fixtures with modern water efficient fixtures and

the addition of new more efficient building stock This back-

ground rate is similarly slowed as the limit is approached

this effect is incorporated by using a percentage-based back-

ground rate Note that price is not explicitly included in this

formulation of demand As stated above because price and

nonprice measures are often implemented in concert it is dif-

ficult to separate the impacts of these two approaches and in

this case unnecessary

dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)

As a comparison a noncoupled model was developed In

this model population and demand changes are no longer

modeled endogenously The shortage awareness variable

is removed as it no longer drives population and demand

changes Instead the model assumes that population growth

is constant at 3 and that per capita demands decrease by

05 annually While these assumptions may be unrealis-

tic they are not uncommon Utility water management plans

typically present one population and one demand projection

Reservoir storage water withdrawals and shortages are com-

puted according to the equations described above A full list

of model variables and parameters can be found in Tables 4

and 5 respectively

33 Results

The model was run for SOP (KP = 1) and three levels of HP

where level one (KP = 15) is the least conservative level

two (KP = 2) is slightly more conservative and level three

(KP = 3) is the most conservative hedging rule tested Three

trials were conducted with a constant parameter set to under-

stand the system variation driven by the stochastic stream-

flow sequence and to test if the relationship hypothesized

was influential across hydrological conditions For each trial

streamflow reservoir storage shortage awareness per capita

demand population and total demand were recorded and

plotted As a comparison each trial was also run in the non-

coupled model in which demand and population changes are

exogenous

In the first trial shown in Fig 6a there were two sus-

tained droughts in the study period from years 5 to 11 and

then from years 33 to 37 Higher than average flows in the

years preceding the first drought allowed the utility to build

up stored water as seen in Fig 6b The storage acts as a buffer

and the impacts are not passed along to the water users until

year 18 under SOP Under HP the impacts as well as wa-

ter usersrsquo shortage awareness increase in years 15 13 and

12 based on the level of the hedging rule (slope of KP) ap-

plied as shown in Fig 6c The impact of this rising shortage

awareness on per capita water demands is seen in the accel-

eration of the decline in demands in Fig 6d This demand

decrease is driven by city level policy changes such as price

increases and voluntary restrictions in combination with in-

creased willingness to conserve

The impacts of this decrease on individual water users will

depend on their socio-economic characteristics as well as the

particular policies implemented While the aggregation hides

this heterogeneity it should be considered in the interpreta-

tion of these results The increased shortage awareness also

has a small dampening effect on population growth during

and directly after the first drought (Fig 6e) Changes to both

per capita demands and population result in total demand

changes (see Fig 6f) After the first drought the system be-

gins to recover under each of the three hedging policies as

evidenced by the slow increase in reservoir storage How-

ever as streamflows fluctuate around average streamflow and

total demands now surpass the average allocation reservoir

storage does not recover when no hedging restrictions are



Figure 6 Model results trial 1 (a) annual streamflow (b) reser-

voir storage volume (c) public shortage awareness (d) per capita

demand (e) annual city population (f) total demand

imposed Several years of above average flow ending in year

29 drive further recovery The second prolonged drought has

the most pronounced effect under the SOP scenario Short-

age impacts are drastic driving further per capita demand

decreases and a temporary decline in population A slight

population decrease is also seen under level one hedging but

the results demonstrate that all hedging strategies dampen the

effect

In the second trial there are two brief droughts in the be-

ginning of the study period beginning in years 4 and 10 as

seen in Fig 7a Under SOP and the first two hedging policies

there is no change in operation for the first drought and the

reservoir is drawn down to compensate as seen in Fig 7andashb

Only under the level three HP are supplies restricted trig-

gering an increase in shortage awareness and a subsequent

decrease in per capita demands as found in Fig 7c and d

When the prolonged drought begins in year 20 the four sce-

narios have very different starting points Under SOP there

is less than 05 km3 of water in storage and total annual de-

mands are approximately 065 km3 In contrast under the

level three HP there is 14 km3 of water in storage and to-

tal annual demands are just under 06 km3 Predictably the

impacts of the drought are both delayed and softened under

HP As the drought is quite severe all scenarios result in a

contraction of population However the rate of decrease and

total population decrease is lowered by the use of HP




In the third and final trial there is no significant low flow

period until year 36 of the simulation when a moderate

drought event occurs as shown in Fig 8a Earlier in the

simulation minor fluctuations in streamflow only trigger an

acceleration of per capita demand declines under the level

three HP as seen in Fig 8c and d A moderate drought begins

in year 36 However the reservoir levels drop and shortage

awareness rise starting before year 20 as seen in Fig 8b and

c Then when the drought occurs the impacts are far greater

than in the comparably moderate drought in trial 1 because a

prolonged period of steady water supply enabled population

growth and placed little pressure on the population to reduce

demands In the SOP scenario the system was in shortage be-

fore the drought occurred and total demands peaked in year

30 at 082 km3 The subsequent drought exacerbated an ex-

isting problem and accelerated changes already in motion

Figure 9 presents results of the noncoupled model simula-

tion While the control model was also run for all three trials

the results of only trial three are included here for brevity

In the noncoupled model HP decreases water withdrawals

as reservoir levels drop and small shortages are seen early

in the study period as seen in Fig 9b and c In the second

half of the study period significant shortages are observed as

in Fig 9c However inspection of the streamflow sequence

reveals no severe low flow periods indicating that the short-

ages are driven by increasing demands as in Fig 9a As ex-






pected changes to per capita demands population and total

demands are gradual and consistent across the operating pol-

icy scenarios found in Fig 9e and f

4 Discussion

The proposed question driven modeling process has three

aims to broaden the researcherrsquos view of the system to

connect modeling assumptions to the modelrsquos purpose and

to increase the transparency of these assumptions A socio-

hydrological model was developed to examine the differ-

ence in long-term reliability between two reservoir operating

policies SOP and HP This question focused the conceptual

model on processes influencing reliability at the city scale

over the 50-year planning period As part of the conceptual

model development the SES framework was used to check

framing assumptions The wide range of candidate variables

included in the SES framework was reviewed against case

data and background information The modelrsquos intended use

then informed decisions of which processes to include in the

model which processes were endogenous to the system and

which variables could be held constant The point here is not

that the logic presented by the modeler using this process

is unfailing but that it is clear and can inform debate The

questions raised about both the functional form of model re-

Figure 9 Noncoupled model results trial 3 (a) annual stream-

flow (b) reservoir storage volume (c) shortage volume (demandndash

supply) (d) per capita demand (e) annual city population (f) total

demand

lationships and the variables excluded during the manuscript

review process indicate that some transparency was achieved

However the reader is in the best position to judge success

on this third aim

A socio-hydrological model of the Sunshine City water

system was developed using the question driven modeling

process and compared to a noncoupled model The noncou-

pled model included assumes that both population growth

and per capita demand change can be considered exogenous

to the system Both models show as prior studies demon-

strated that by making small reductions early on HP re-

duces the chance of severe shortages The socio-hydrological

model also demonstrates that in the HP scenarios the mod-

erate low flow events trigger an acceleration of per capita

demand decrease that shifts the trajectory of water demands

and in some instances slows the rate of population growth

In contrast SOP delays impacts to the water consumers and

therefore delays the shift to lower per capita demands When

extreme shortage events such as a deep or prolonged drought

occur the impacts to the system are far more abrupt in the

SOP scenario because per capita demands and population are

higher than in hedging scenarios and there is less stored water

available to act as a buffer When we compare SOP and HP

using a socio-hydrological model we see that HP decreases

the magnitude of the oscillations in demand and population



Hedging reduces the threshold for action thereby decreasing

the delay and the oscillation effect This distinction between

the two policies was not apparent when using a traditional

noncoupled model The significance of this observation is

that a decrease in oscillation means a decrease in the mag-

nitude of the contractions in population and per capita water

demands required to maintain sustainability of the system It

is these abrupt changes in water usage and population that

water utilities and cities truly want to avoid as they would

hamper economic growth and decrease quality of life

Examining the structure of the system can explain the dif-

ferences in system response to SOP and HP As seen in Fig 5

there are one positive and two negative feedback loops in the

system Positive feedback loops such as population in this

model exhibit exponential growth behavior but there are few

truly exponential growth systems in nature and through in-

teraction with other feedback loops most systems ultimately

reach a limit (Sterman 2000) Negative feedback loops gen-

erate goal seeking behavior In its simplest form a negative

feedback loop produces a slow approach to a limit or goal

akin to an exponential decay function In this case the goal

of the system is to match total demand with average sup-

ply The fact that supply is driven by streamflow a stochastic

variable adds noise to the system Even if streamflow is cor-

rectly characterized with stationary statistics as is assumed

here the variability challenges the management of the sys-

tem Reservoir storage helps utilities manage this variability

by providing a buffer but it also acts as a delay The delay

between a change in the state of the system and action taken

in response allows the system to overshoot its goal value be-

fore corrective action is taken leading to oscillation around

goal values While water storage decreases the impact of a

drought changes to water consumption patterns are required

to address demand driven shortages Water storage simulta-

neously buffers variability and delays water user response by

delaying impact There are parallels between the feedback

identified in this urban water supply system and the feedback

identified by Elshafei et al (2014) and Di Baldassarre (2013)

in agricultural water management and humanndashflood interac-

tions respectively Broadly the three systems display the bal-

ance between the interaction between opposing forces in this

case articulated as positive and negative feedback loops

The case of Sunshine City is simplified and perhaps sim-

plistic The limited number of available options for action

constrains the system and shapes the observed behavior In

many cases water utilities have a portfolio of supply stor-

age and demand management policies to minimize short-

ages Additionally operating policies often shift in response

to changing conditions However in this case no supply side

projects are considered and the reservoir operating policy is

assumed constant throughout the duration of the study pe-

riod As there are physical and legal limits to available sup-

plies the first constraint reflects the reality of some systems

Constant operational policy is a less realistic constraint but

can offer new insights by illustrating the limitations of main-

taining a given policy and the conditions in which policy

change would be beneficial Despite these drawbacks a sim-

ple hypothetical model is justified here to clearly illustrate

the proposed modeling process

There are several limitations to the hypothetical case of

Sunshine City First the hypothetical nature of the case pre-

cludes hypothesis testing Therefore an important extension

of this work will be to apply the modeling process pre-

sented here on a real case to fully test the resulting model

against historical observations before generating projections

Second only one set of parameters and functions was pre-

sented Future extensions to this work on reservoir policy

selection will test the impact of parameter and function se-

lection through sensitivity analysis Finally we gain limited

understanding of the potential of the model development pro-

cess by addressing only one research question We can fur-

ther test the ability of the modeling process to generate new

insights by developing different models in response to dif-

ferent questions In this case the narrow scope of the driv-

ing question leads to a model that just scratches the surface

of socio-hydrological modeling as evidenced by the narrow

range of societal variables and processes included For exam-

ple this model does not address the ability of the water utility

or city to adopt or implement HP HP impacts water users in

the short term These impacts would likely generate a mix

of reactions from water users and stakeholders making it im-

possible to ignore politics when considering the feasibility of

HP However the question driving this model asks about the

impact of a policy choice on the long-term reliability of the

system not the feasibility of its implementation A hypothe-

sis addressing the feasibility of implementation would lead

to a very different model structure

While there is significant room for improvement there are

inherent limitations to any approach that models human be-

havior The human capacity to exercise free will to think

creatively and to innovate means that human actions particu-

larly under conditions not previously experienced are funda-

mentally unpredictable Furthermore as stated above we can

never fully capture the complexity of the socio-hydrological

system in a model Instead we propose a modeling process

that focuses socio-hydrological model conceptualization on

answering questions and solving problems By using model

purpose to drive our modeling decisions we provide justi-

fication for simplifying assumptions and a basis for model

evaluation

5 Conclusions

Human and water systems are coupled The feedback be-

tween these two subsystems can be but are not always

strong and fast enough to warrant consideration in water

planning and management Traditional noncoupled model-

ing techniques assume that there is no significant feedback

between human and hydrological systems They therefore



offer no insights into how changes in one part of the sys-

tem may affect another Dynamic socio-hydrological model-

ing recognizes and aims to understand the potential for feed-

backs between human and hydrological systems By building

human dynamics into a systems model socio-hydrological

modeling enables testing of hypothesized feedback cycles

and can illuminate the way changes propagate through the

coupled system

Recent work examining a range of socio-hydrological

systems demonstrates the potential of this approach How-

ever there are significant challenges to modeling socio-

hydrological systems First there are no widely accepted

laws of human systems as there are for physical or chemical

systems Second common disciplinary assumptions must be

questioned due to the integrative nature of socio-hydrology

Transparency of the model development process and assump-

tions can facilitate the replication and critique needed to

move this young field forward We assess the progress and

gaps in socio-hydrological modeling and draw lessons from

adjacent fields of study hydrology social-ecological systems

science and system dynamics to inform a question driven

model development process We then illustrate this process

by applying it to the hypothetical case of a growing city ex-

ploring two alternate reservoir operation rules

By revisiting the classic question of reservoir operation

policy we demonstrate the utility of a socio-hydrological

modeling process in generating new insights into the im-

pacts of management practices over decades This socio-

hydrological model shows that HP offers an advantage not

detected by traditional simulation models it decreases the

magnitude of the oscillation effect inherent in goal seeking

systems with delays Through this example we identify one

class of question the impact of reservoir management policy

selection over several decades for which socio-hydrological

modeling offers advantages over traditional modeling The

model developed and the resulting insights are contingent

upon the question context The dynamics identified here may

be more broadly applicable but this is for future cases and

models to assess

The Supplement related to this article is available online

at doi105194hess-20-73-2016-supplement

Acknowledgements We would like to thank Brian Fath Wei Liu

and Arnold Vedlitz for reviewing an early version of this paper We

would also like to thank the two reviewers for their careful reading

and thoughtful comments Financial support for this research

comes from the NSF Water Diplomacy IGERT grant (0966093)

Edited by M Sivapalan

References

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2015 2015

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ing forest and impervious land covers on discharge characteris-

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theoretical analysis Water Resour Res 44 1ndash9 2008

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in environmental modelling Occamrsquos razor revisited J Appl

Stat 23 165ndash210 doi10108002664769624206 1996

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Department of Agriculture Washington DC 1992


Abstract

Introduction

Modeling socio-hydrological systems

Modeling hydrological systems

Modeling coupled systems

Progress and gaps in socio-hydrological modeling

A question driven modeling process

Sunshine City a case study of reservoir operations

Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References


Human and hydrological systems are coupled Many im-

pacts of human activity on the hydrological system are now

well documented (Tong and Chen 2002 Wissmar et al

2004 Voumlroumlsmarty et al 2010 Vahmani and Hogue 2014)

and there is increasing evidence that how and when hu-

mans respond individually and collectively to hydrological

change has important implications for water resources plan-

ning management and policy (Srinivasan et al 2010 Di

Baldassarre et al 2013 Elshafei et al 2014) These obser-

vations have prompted a call to treat humans as an endoge-

nous component of the water cycle (Wagener et al 2010

Sivapalan et al 2012) Representing water systems as cou-

pled humanndashhydrological systems or socio-hydrological sys-

tems with two-way feedback allows new research questions

and potentially transformative insights to emerge

Traditional modeling approaches assume that there is no

feedback between hydrological and human systems and

therefore cannot provide insights into how different patterns

of natural variability or human-induced change may prop-

agate through the coupled system Over short timescales

such as a year many human and hydrological variables

can be considered constant and their couplings may be ig-

nored (Srinivasan 2015) However water resources infras-

tructure decisions have impacts on longer (decadal to cen-

tury) timescales therefore there is a need for an approach

that can handle not only long-term variability and nonsta-

tionarity in the driving variables (eg precipitation temper-

ature population) but also addresses how these changes can

propagate through the coupled system affecting the struc-

ture and properties of the coupled system (Sivapalan et al

2012 Thompson et al 2013) Dynamic modeling of socio-

hydrological systems recognizes the potential for humans to

transform hydrological systems and for hydrological condi-

tions to influence human behavior While human behavior

is usually incorporated into a model through scenarios sce-

narios cannot include two-way feedback Building effects of

human behavior into a simulation model can enable testing

of feedback cycles and can illuminate the impact of feed-

back and path dependencies that are not easily identifiable in

scenario-based modeling

Coupled modeling on the other hand introduces new

challenges First it is not possible to exhaustively model

complex systems such as the coupled humanndashhydrological

system (Sterman 2000 Schluumlter et al 2014) Bounds must

be set to develop an effective model but researchers are chal-

lenged to objectively define the scope of coupled modeling

studies Second by definition coupled models cross disci-

plines and modelers are unable to point to the theoretical

framework of any single discipline to defend the relevant

scope (Srinivasan 2015) At the same time researchers must

balance the scope and level of detail in order to create a

parsimonious and communicable model Finally critical as-

sessment of models is more challenging when the theories

empirical methods and vocabulary drawn upon to create and

communicate a model span disciplinary boundaries (Schluumlter

et al 2014) At the same time critique is needed to move

the field forward as the science is new and lacks established

protocols Transparency of the model aims the development

process conceptual framework and assumptions are thus par-

ticularly important A structured but flexible modeling pro-

cess can address these challenges by encouraging modelers

to clearly define model objectives document reasoning be-

hind choices of scale scope and detail and take a broad view

of potentially influential system processes

In this paper we present a question driven process for mod-

eling socio-hydrological systems that builds on current mod-

eling tools from both domains and allows the flexibility for

exploration We demonstrate this process by revisiting a clas-

sic question in water resources engineering on reservoir op-

eration rules the tradeoff between standard operating policy

(SOP) and hedging policy (HP) Under SOP demand is ful-

filled unless available supply drops below demand under HP

water releases are reduced in anticipation of a deficit to de-

crease the risk a large shortfall (Cancelliere et al 1998) We

add to this classic question a linkage between supply relia-

bility and demand As this question has been asked by nu-

merous researchers before it offers an excellent opportunity

to test the utility of our proposed modeling framework using

a hypothetical municipality called Sunshine City as a case

study

2 Modeling socio-hydrological systems

Modeling the interactions between human and hydrological

systems exacerbates challenges found in modeling purely hy-

drological systems including setting the model boundary de-

termining the relevant processes and relationships and clearly

communicating model framing and assumptions Common

approaches to hydrological modeling are reviewed to put

socio-hydrological modeling in the context of hydrological

modeling practice Next modeling approaches used in sys-

tem dynamics and social-ecological systems science both

of which address coupled systems are described Then

socio-hydrological modeling approaches are reviewed and

gaps identified While no one approach is directly trans-

ferrable to socio-hydrological systems practices from hy-

drological modeling along with those from integrative dis-

ciplines serve as a baseline for comparison and inform our

socio-hydrological modeling process We then present our

recommendations for socio-hydrological model conceptual-

ization

21 Modeling hydrological systems

In hydrology the basic steps of model development are

(a) data collection and analysis (b) conceptual model devel-

opment (c) translation of the conceptual model to a mathe-

matical model (d) model calibration and (e) model valida-

tion (Bloumlschl and Sivapalan 1995) While the basic steps








































proposed process






























































et al 2010 2013)































































































parison






































assumptions









































RESEARCH QUESTION

CONCEPTUAL MODEL


PROCESSES


WAR

D RE

ASO

NIN

G

PROCESSES


OUTCOME INDICATORS

FORW

ARD

REAS

ON

ING


al 2014)































































model processes

































































bility











LEAS

E


DP

DP VMAX + DP

1

1

1

1



and ReVelle 1994)

31 Background





















Water 2015)
















RELE

ASE


DP

KPDP VMAX + DP

KP

1

1

1














lection































(ISTPP 2013)





















































































water demands























0

50

100

150

200

1970 1980 1990 2000 2010Year

Per

cap

ita d

eman

d (g

allo

ns p

er d

ay)






dominate





































framework



















variables



















































RS9 ndash Location

















A4 ndash Location




























Reservoir storage

Shortageawareness

Waterdemand

Water supply

Water shortage

+

-

+

-

-

-

Reservoirstorage

Shortageawareness


Water shortage

+

-

+

-

-

Population

-


+

+


and growth rate































































(1minusp2

H

)05

at +microH (1)




























dV





























dP

dt=


(3)














DtPt +Vmax


Vt + 025Qtminus1

KP




St =


0 otherwise(5)
























dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References







































proposed process






























































et al 2010 2013)































































































parison






































assumptions









































RESEARCH QUESTION

CONCEPTUAL MODEL


PROCESSES


WAR

D RE

ASO

NIN

G

PROCESSES


OUTCOME INDICATORS

FORW

ARD

REAS

ON

ING


al 2014)































































model processes

































































bility











LEAS

E


DP

DP VMAX + DP

1

1

1

1



and ReVelle 1994)

31 Background





















Water 2015)
















RELE

ASE


DP

KPDP VMAX + DP

KP

1

1

1














lection































(ISTPP 2013)





















































































water demands























0

50

100

150

200

1970 1980 1990 2000 2010Year

Per

cap

ita d

eman

d (g

allo

ns p

er d

ay)






dominate





































framework



















variables



















































RS9 ndash Location

















A4 ndash Location




























Reservoir storage

Shortageawareness

Waterdemand

Water supply

Water shortage

+

-

+

-

-

-

Reservoirstorage

Shortageawareness


Water shortage

+

-

+

-

-

Population

-


+

+


and growth rate































































(1minusp2

H

)05

at +microH (1)




























dV





























dP

dt=


(3)














DtPt +Vmax


Vt + 025Qtminus1

KP




St =


0 otherwise(5)
























dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References
























































































parison






































assumptions









































RESEARCH QUESTION

CONCEPTUAL MODEL


PROCESSES


WAR

D RE

ASO

NIN

G

PROCESSES


OUTCOME INDICATORS

FORW

ARD

REAS

ON

ING


al 2014)































































model processes

































































bility











LEAS

E


DP

DP VMAX + DP

1

1

1

1



and ReVelle 1994)

31 Background





















Water 2015)
















RELE

ASE


DP

KPDP VMAX + DP

KP

1

1

1














lection































(ISTPP 2013)





















































































water demands























0

50

100

150

200

1970 1980 1990 2000 2010Year

Per

cap

ita d

eman

d (g

allo

ns p

er d

ay)






dominate





































framework



















variables



















































RS9 ndash Location

















A4 ndash Location




























Reservoir storage

Shortageawareness

Waterdemand

Water supply

Water shortage

+

-

+

-

-

-

Reservoirstorage

Shortageawareness


Water shortage

+

-

+

-

-

Population

-


+

+


and growth rate































































(1minusp2

H

)05

at +microH (1)




























dV





























dP

dt=


(3)














DtPt +Vmax


Vt + 025Qtminus1

KP




St =


0 otherwise(5)
























dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References














assumptions









































RESEARCH QUESTION

CONCEPTUAL MODEL


PROCESSES


WAR

D RE

ASO

NIN

G

PROCESSES


OUTCOME INDICATORS

FORW

ARD

REAS

ON

ING


al 2014)































































model processes

































































bility











LEAS

E


DP

DP VMAX + DP

1

1

1

1



and ReVelle 1994)

31 Background





















Water 2015)
















RELE

ASE


DP

KPDP VMAX + DP

KP

1

1

1














lection































(ISTPP 2013)





















































































water demands























0

50

100

150

200

1970 1980 1990 2000 2010Year

Per

cap

ita d

eman

d (g

allo

ns p

er d

ay)






dominate





































framework



















variables



















































RS9 ndash Location

















A4 ndash Location




























Reservoir storage

Shortageawareness

Waterdemand

Water supply

Water shortage

+

-

+

-

-

-

Reservoirstorage

Shortageawareness


Water shortage

+

-

+

-

-

Population

-


+

+


and growth rate































































(1minusp2

H

)05

at +microH (1)




























dV





























dP

dt=


(3)














DtPt +Vmax


Vt + 025Qtminus1

KP




St =


0 otherwise(5)
























dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References



























model processes

































































bility











LEAS

E


DP

DP VMAX + DP

1

1

1

1



and ReVelle 1994)

31 Background





















Water 2015)
















RELE

ASE


DP

KPDP VMAX + DP

KP

1

1

1














lection































(ISTPP 2013)





















































































water demands























0

50

100

150

200

1970 1980 1990 2000 2010Year

Per

cap

ita d

eman

d (g

allo

ns p

er d

ay)






dominate





































framework



















variables



















































RS9 ndash Location

















A4 ndash Location




























Reservoir storage

Shortageawareness

Waterdemand

Water supply

Water shortage

+

-

+

-

-

-

Reservoirstorage

Shortageawareness


Water shortage

+

-

+

-

-

Population

-


+

+


and growth rate































































(1minusp2

H

)05

at +microH (1)




























dV





























dP

dt=


(3)














DtPt +Vmax


Vt + 025Qtminus1

KP




St =


0 otherwise(5)
























dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References


LEAS

E


DP

DP VMAX + DP

1

1

1

1



and ReVelle 1994)

31 Background





















Water 2015)
















RELE

ASE


DP

KPDP VMAX + DP

KP

1

1

1














lection































(ISTPP 2013)





















































































water demands























0

50

100

150

200

1970 1980 1990 2000 2010Year

Per

cap

ita d

eman

d (g

allo

ns p

er d

ay)






dominate





































framework



















variables



















































RS9 ndash Location

















A4 ndash Location




























Reservoir storage

Shortageawareness

Waterdemand

Water supply

Water shortage

+

-

+

-

-

-

Reservoirstorage

Shortageawareness


Water shortage

+

-

+

-

-

Population

-


+

+


and growth rate































































(1minusp2

H

)05

at +microH (1)




























dV





























dP

dt=


(3)














DtPt +Vmax


Vt + 025Qtminus1

KP




St =


0 otherwise(5)
























dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References



(ISTPP 2013)





















































































water demands























0

50

100

150

200

1970 1980 1990 2000 2010Year

Per

cap

ita d

eman

d (g

allo

ns p

er d

ay)






dominate





































framework



















variables



















































RS9 ndash Location

















A4 ndash Location




























Reservoir storage

Shortageawareness

Waterdemand

Water supply

Water shortage

+

-

+

-

-

-

Reservoirstorage

Shortageawareness


Water shortage

+

-

+

-

-

Population

-


+

+


and growth rate































































(1minusp2

H

)05

at +microH (1)




























dV





























dP

dt=


(3)














DtPt +Vmax


Vt + 025Qtminus1

KP




St =


0 otherwise(5)
























dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References


0

50

100

150

200

1970 1980 1990 2000 2010Year

Per

cap

ita d

eman

d (g

allo

ns p

er d

ay)






dominate





































framework



















variables



















































RS9 ndash Location

















A4 ndash Location




























Reservoir storage

Shortageawareness

Waterdemand

Water supply

Water shortage

+

-

+

-

-

-

Reservoirstorage

Shortageawareness


Water shortage

+

-

+

-

-

Population

-


+

+


and growth rate































































(1minusp2

H

)05

at +microH (1)




























dV





























dP

dt=


(3)














DtPt +Vmax


Vt + 025Qtminus1

KP




St =


0 otherwise(5)
























dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References



















RS9 ndash Location

















A4 ndash Location




























Reservoir storage

Shortageawareness

Waterdemand

Water supply

Water shortage

+

-

+

-

-

-

Reservoirstorage

Shortageawareness


Water shortage

+

-

+

-

-

Population

-


+

+


and growth rate































































(1minusp2

H

)05

at +microH (1)




























dV





























dP

dt=


(3)














DtPt +Vmax


Vt + 025Qtminus1

KP




St =


0 otherwise(5)
























dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References


Reservoir storage

Shortageawareness

Waterdemand

Water supply

Water shortage

+

-

+

-

-

-

Reservoirstorage

Shortageawareness


Water shortage

+

-

+

-

-

Population

-


+

+


and growth rate































































(1minusp2

H

)05

at +microH (1)




























dV





























dP

dt=


(3)














DtPt +Vmax


Vt + 025Qtminus1

KP




St =


0 otherwise(5)
























dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References























dV





























dP

dt=


(3)














DtPt +Vmax


Vt + 025Qtminus1

KP




St =


0 otherwise(5)
























dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References




















dM

dt=

(St

DtPt

)2





























dD

dt=minusDt

[Mtα

(1minus

Dmin

Dt

)+β

](7)













and 5 respectively

33 Results













exogenous










































effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References












effect
























































4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References








4 Discussion























demand




on this third aim



























































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References





































































































evaluation

5 Conclusions
















coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References









coupled system































models to assess









References










hav 24 602ndash616 1992








doi101098rspa20020986 2002




2015 2015



doi101002hyp3360090305 1995














148 1998






doi101111j1541-1338201000443x 2010




doi1023073146872 2003




75 doi101016jjenvman201210015 2013



2015






doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References



doi105194hess-17-3295-2013 2013





doi1010022014WR016416 2015







2014 2014





doi1010022015WR017048 2015






sour Res 48 W10510 doi1010292012WR012398 2012






2004









554ndash564 2013



doi10108002508060008686804 2000




2015




SP408-2 2014










doi1010022014EF000295 2015







doi101016jcities201302007 2013

















doi105194hess-18-1027-2014 2014













3568(2005)055[0967PI]20CO2 2005





2014 2014



WR017002 1010022015WR017002 2015




doi101016jjenvman201010037 2011








218ndash228 2009





0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References




0072201000396xfull 2011




0072201000401x 2011b



30 doi105751ES-06387-190230 2014









cess 1 July 2015) 2003



W04301 doi1010292008WR007227 2009





doi101126science1172133 2009





Ecol Soc 12 5 2007






W12529 doi1010292012WR012335 2012







doi101111j1540-6210201102367x 2011




05782-190136 2014



1172ndash1193 2013



1994




doi1010022015WR017080 2015



WR017896 doi1010022015WR017896 2015



2111 doi101002hyp1425 2003



26 1270ndash1276 2012







doi1010292009WR008698 2010





doi101016jgloenvcha201210002 2013




19-785-2015 2015




4797(02)00205-0 2003








2013 2013



2002




51 WR017046 doi1010022015WR017046 2015




tute London 1998










2014 2014












doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References











doi101038nature09549 2010




Res 46 W05301 doi1010292009WR008906 2010




1993












Stat 23 165ndash210 doi10108002664769624206 1996



17 2195ndash2217 doi101002hyp1328 2003






Abstract

Introduction







Background

Model development

Results

Discussion

Conclusions

Acknowledgements

References

a question driven socio-hydrological modeling process · human and hydrological systems are...

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